This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288424 #35 Mar 12 2025 04:40:52 %S A288424 0,0,1,0,1,0,0,1,0,2,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0, %T A288424 1,0,0,1,0,1,0,0,2,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0,1,2,0,0,1, %U A288424 0,1,2,0,0,0,1,0,0,0,0,1,0,2,2,0,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,1 %N A288424 Partial sums of A288384. %C A288424 It appears that the number of zeros is infinite. %C A288424 Observation: for at least the first 110 terms the largest distance between two zeros that are between nonzero terms is 3. %C A288424 Question: are there distances > 3? %C A288424 From _Hartmut F. W. Hoft_, Jun 13 2017: (Start) %C A288424 Yes: a(346..351) = (0,1,2,3,4,0). %C A288424 Conjecture: a(n) >= 0 for all n >= 0, and a(n) is unbounded. %C A288424 First occurrences: 3 = a(337) occurring 27 times; 4 = a(350) occurring 8 times; 5 = a(830) occurring 5 times; all through n=2500. (End) %t A288424 (* function a288384[] is defined in A288384 *) %t A288424 a288424[n_] := Accumulate[a288384[n]] %t A288424 a288424[104] (* data *) (* _Hartmut F. W. Hoft_, Jun 13 2017 *) %Y A288424 Cf. A274650, A286294, A288384. %K A288424 nonn %O A288424 0,10 %A A288424 _Omar E. Pol_, Jun 09 2017 %E A288424 Signs reversed at the suggestion of _Hartmut F. W. Hoft_ by _Omar E. Pol_, Jun 13 2017